Johnson answered with a layup, Gay hit a turnaround jumper and DeRozan banked in a jump shot as Toronto opened a 10-point cushion, 90-80, with 2:34 left.
Faverani scored nine points in the first and the Celtics made 11 of 17 field goal attempts to lead 26-21 after one quarter.
Boston went cold to start the second, missing eight of their first nine attempts and allowing Toronto to take the lead with an 8-1 run.
The Celtics made just two of 14 shots in the second, while the Raptors got six points from Terrence Ross and four each from Gay and Johnson to lead 49-37 at the half.
Toronto extended its lead to 16 points at 60-44 on a Valanciunas dunk at 8:18 of the third, but the Celtics rallied behind nine points from Green and 10 from Bass, whose buzzer-beating dunk knotted the score at 71-all.
NOTES: Boston forward Jared Sullinger served a one-game team suspension, two days after a judge dismissed domestic violence charges against him. ... Toronto outrebounded Boston 48-33. ... Singer Jon Bon Jovi and former Raptors star Morris Peterson attended the game.